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Simplifying x4 + x2 + -1946546 = 0 Reorder the terms: -1946546 + x2 + x4 = 0 Solving -1946546 + x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1946546' to each side of the equation. -1946546 + x2 + 1946546 + x4 = 0 + 1946546 Reorder the terms: -1946546 + 1946546 + x2 + x4 = 0 + 1946546 Combine like terms: -1946546 + 1946546 = 0 0 + x2 + x4 = 0 + 1946546 x2 + x4 = 0 + 1946546 Combine like terms: 0 + 1946546 = 1946546 x2 + x4 = 1946546 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x2 + 0.25 + x4 = 1946546 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 1946546 + 0.25 Combine like terms: 1946546 + 0.25 = 1946546.25 0.25 + x2 + x4 = 1946546.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 1946546.25 Calculate the square root of the right side: 1395.186815448 Break this problem into two subproblems by setting (x2 + 0.5) equal to 1395.186815448 and -1395.186815448.Subproblem 1
x2 + 0.5 = 1395.186815448 Simplifying x2 + 0.5 = 1395.186815448 Reorder the terms: 0.5 + x2 = 1395.186815448 Solving 0.5 + x2 = 1395.186815448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 1395.186815448 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 1395.186815448 + -0.5 x2 = 1395.186815448 + -0.5 Combine like terms: 1395.186815448 + -0.5 = 1394.686815448 x2 = 1394.686815448 Simplifying x2 = 1394.686815448 Take the square root of each side: x = {-37.345505961, 37.345505961}Subproblem 2
x2 + 0.5 = -1395.186815448 Simplifying x2 + 0.5 = -1395.186815448 Reorder the terms: 0.5 + x2 = -1395.186815448 Solving 0.5 + x2 = -1395.186815448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -1395.186815448 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -1395.186815448 + -0.5 x2 = -1395.186815448 + -0.5 Combine like terms: -1395.186815448 + -0.5 = -1395.686815448 x2 = -1395.686815448 Simplifying x2 = -1395.686815448 Reorder the terms: 1395.686815448 + x2 = -1395.686815448 + 1395.686815448 Combine like terms: -1395.686815448 + 1395.686815448 = 0.000000000 1395.686815448 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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